Your phone will pick up whatever is the strongest signal. If there is no 4G signal it will "step down" to 3G and if no 3G it will keep stepping down until it either finds a signal it can use or will show 'No Service'.
The issue of battery draw comes in to play when your phone is trying to hold on to a weak signal. That results in the phone hammering the tower it's connected to in order to stay connected, which in turn causes battery draw because the phone is active.
If your area does have weak 4G signal though and it's not useable, then yeah, I'd turn it off.
